Arguments

Obj

The function requires either a Txn matrix or an object with class "‘Eup"’ or "‘KSS"’.

criteria

A character vector that contains the desired criteria to be used. If it is left unspecified, the function returns the result of all 16 criteria.

standardize

logical. If TRUE the input variable will be standardized. Default is FALSE.

d.max

Maximal dimension used in the dimensionality-criteria of Bai
(2009). The default (d.max=NULL) yields to an internal selection of
d.max.

sig2.hat

The squared standard deviation of the error-term required for the computation of some dimensionality criteria. The user can specify it in instead of d.max. The default (sig2.hat=NULL) yields to an internal estimation.

spar

Smoothing parameter used to calculate the criterion of Kneip, Sickles, and Song (2012). The default is NULL, which leads to internal computation.

level

The significance level used for the criterion of Kneip, Sickles, and Song (2012). The default is 0.01.

c.grid

Required only for computing "ABC.IC1" and "ABC.IC2". It specifies the grid interval in which the scaling parameter of the penalty terms in "ABC.IC1" and "ABC.IC2" are calibrated. Default is c.grid =seq(0, 5, length.out = 128).

T.seq

Required only for computing "ABC.IC1" and "ABC.IC2". It can be a vector containing different dimensions for T or an integer indicating the length of the sequence to be considered in calibrating "ABC.IC1" and "ABC.IC2". If it is left unspecified, the function determines internally a sequence of the form seq((T-C), T), where C is the square root of min{T,900}.

n.seq

Required only for computing "ABC.IC1" and "ABC.IC2". It can be a vector containing different dimensions for n or an integer indicating the length of the sequence to be considered in calibrating "ABC.IC1" and "ABC.IC2". If it is left unspecified, the function determines internally a sequence of the form seq((n-D), n), where D is the square root of min{n,900}.

Details

The function 'OptDim' allows for a comparison of the optimal factor dimensions obtained from different panel criteria (in total 13). This criteria are adjusted for panel data with diverging T and N.

Value

'OptDim' returns an object of 'class' '"OptDim"' containing a list with the
following components:

criteria:

The name of the criteria specified by the user.

PC1:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

PC2:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

PC3:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

IC1:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max.

IC2:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max.

IC3:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max.

IPC1:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

IPC2:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

IPC3:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

KSS.C:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max and/ or sig2.hat.

ED:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max.

ER:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max.

GR:

If specified in criteria a table is returned with the optimal dimension, the empirical standard deviation of the residuals, and some other informations required internally by the criterion, such as d.max.

summary:

A table (in a matrix form) containing all the estimated dimensions obtained by the specified criteria.

Onatski, A. 2010 “Determining the number of factors from empirical distribution of eigenvalues”, The Review of Economics and Statistics

Examples

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## See the example in 'help(Cigar)' in order to take a look at the## data set 'Cigar'############ DATA ############data(Cigar)
N <-46T<-30## Data: Cigarette-Sales per Capita
l.Consumption <-log(matrix(Cigar$sales,T,N))## Calculation is based on the covariance matrix of l.ConsumptionOptDim(l.Consumption)## Calculation is based on the correlation matrix of l.ConsumptionOptDim(l.Consumption,standardize=TRUE)## Display the magnitude of the eigenvalues in percentage of the total varianceplot(OptDim(l.Consumption))